Insignificant value

Question

Let us say that a line is defined as $$ y=\frac{\sqrt{c^2-a^2}}{a}x $$ and $a<c$. Can we tell when the value of $a$ becomes insignificant with respect to $c$?

Answer 1

You probably mean that if we keep increasing $c$ and keep $a$ constant, when can we ignore $a$. This is usually done in science where we need to approximate things and it us upto us what degree of accuracy we want. There is no such standard where we can say that $c >>a$.

However, suppose if $c=100$ and $a=1$, for calculation purposes, we may simply write your expression as $$y=\dfrac{\sqrt{10000-1}}{1}x\approx \sqrt{10000}x=100x$$

Which differs from actual answer by roughly $0.005x.$ Now it is upto you to accept it or not.